Hi Márcio!
Please, no need to ask for forgiveness for just trying to figure out English prepositions! Just take a look at my attempts to write Portuguese . . .
I don't know what Google turned up for you. Let me tell you, as I browse the internet sometimes I see A LOT of mistakes made in English that has apparently been written by a non-native speaker/writer. So, just because it's on the internet (or on TV or radio) doesn't mean it is correct English.
That said, the expression goes "too much time on my hands" [on your hands, on his hands, etc.] and the preposition used in the expression is "on."
I will think up a few sentences with the noun "time":
I have spent a lot of time thinking of you. ["thinking about you" is okay in this sentence also]
When I went to Brazil, I spent some time in Maceió.
If I leave the house now, I think I will get there in time. (Acho que vou chegar "na hora" is how I think it is expressed in Portuguese.
In time, you will learn to have patience in these matters.
So, let's see, in every instance here I have used the preposition "in" with time. Then, this phrase "time on my hands" must be separated grammatically as "time" + "on my hands," and the preposition makes more sense here:
How did you get that paint on your hands?
He wrote the answers to the test on his hand.
There, see, we figured it out together :) :) :) Didn't we?
Hope this helps, Márcio. Too bad I'm not a teacher or I could explain things better. I have to work these things through.
Um forte abraço,
Ana